Prove (cosecθ-cotθ)^2=1-cosθ÷1+cosθ

Answer 1

I will assume that you meant:
(cosecθ-cotθ)^2=(1-cosθ)÷(1+cosθ)
or else the identity is not true.

LS = (1/sinØ - cosØ/sinØ)2
= (1-cosØ)^2 / sin^2 Ø
= (1 - cosØ)(1-cosØ)/( (1 - cosØ)(1 + cosØ) )
= (1 - cosØ)/(1+cosØ)

= RS